Annealed transition density of simple random walk on a high-dimensional loop-erased random walk

2023/12/15 by David A. Croydon, Croydon, David A., Daisuke Shiraishi +3
Computer Science · Mathematics · #05C81 #60J35 #60K35 #60K37 (primary) #82B41 #Bayesian Methods and Mixture Models #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2312.09522

openalex publication_date 2023/12/15 · openalex created_date 2023/12/19 · openalex updated_date 2026/07/28

Abstract

We derive sub-Gaussian bounds for the annealed transition density of the simple random walk on a high-dimensional loop-erased random walk. The walk dimension that appears in these is the exponent governing the space-time scaling of the process with respect to the extrinsic Euclidean distance, which contrasts with the exponent given by the intrinsic graph distance that appears in the corresponding quenched bounds. We prove our main result using novel pointwise Gaussian estimates on the distribution of the high-dimensional loop-erased random walk.

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